
Mark Spahn writes:
Numerical comparisons: "three times ~er than" versus
"three
times as ~ as"
"Arab isolation has exacted a heavy economic cost.
Algeria was only very slightly poorer than Portugal in 1960; today
Portugal is three times richer than Algeria. Syria was a
substantially wealthier country than South Korea in 1960; today, South
Korea is more than five times richer." (An End to
Evil: How to Win the War on Terror, by David Frum and Richard
Perle, page 170)
This quotation makes a numerical comparison between pairs of numbers
that measure the richness of countries, such as their average
percapita annual income.
To say that "Portugal is three times as rich as Algeria" means
numerically that P = 3 ~ A, where P and A
are the average percapita
annual income of Portugal and Algeria, respectively.
To say that "Portugal is 300 percent richer than Algeria" means that P
= A + (300% of A) = A + (3.00 ~ A) = 4
~ A. But P = 4 ~ A, translated
back into nonmathematical wording, means that "Portugal is four times
as rich as Algeria."
What does it mean to say that "Portugal is three times richer than
Algeria"? There are two possibilities:
(1) P = A + (3 ~ A) = 4 ~ A.
Since "three times" means the same as
"300 percent," "three times richer" should mean "300 percent richer,"
and,
by the above argument, "300 percent richer" means the same as "four
times
as rich."
(2) P = 3 ~ A. By this interpretation, "three
times richer" means
the same as "three times as rich."
Which interpretation of "three times richer" is right? Logically,
interpretation (1) is correct, but in practice, a Google search of "N
times ~er than" would find that interpretation (2) is adopted by almost
all of the examples that include enough information to resolve the
numerical relationship between the two compared quantities.
(June 4, 2004)

